qiskit.opflow.list_ops.ListOp¶

class
ListOp
(oplist, combo_fn=None, coeff=1.0, abelian=False, grad_combo_fn=None)[source]¶ A Class for manipulating List Operators, and parent class to
SummedOp
,ComposedOp
, andTensoredOp
.List Operators are classes for storing and manipulating lists of Operators, State functions, or Measurements, and include some rule or
combo_fn
defining how the Operator functions of the list constituents should be combined to form to cumulative Operator function of theListOp
. For example, aSummedOp
has an additionbasedcombo_fn
, so once the Operators in its list are evaluated against some bitstring to produce a list of results, we know to add up those results to produce the final result of theSummedOp
’s evaluation. In theory, thiscombo_fn
can be any function over classical complex values, but for convenience we’ve chosen for them to be defined over NumPy arrays and values. This way, large numbers of evaluations, such as after callingto_matrix
on the list constituents, can be efficiently combined. While the combination function is defined over classical values, it should be understood as the operation by which each Operators’ underlying function is combined to form the underlying Operator function of theListOp
. In this way, theListOps
are the basis for constructing large and sophisticated Operators, State Functions, and Measurements.The base
ListOp
class is particularly interesting, as itscombo_fn
is “the identity list Operation”. Meaning, if we understand thecombo_fn
as a function from a list of complex values to some output, one such function is returning the list asis. This is powerful for constructing compact hierarchical Operators which return many measurements in multiple dimensional lists. Parameters
oplist (
Sequence
[OperatorBase
]) – The list ofOperatorBases
defining this Operator’s underlying function.combo_fn (
Optional
[Callable
]) – The recombination function to combine classical results of theoplist
Operators’ eval functions (e.g. sum). Default is lambda x: x.coeff (
Union
[complex
,ParameterExpression
]) – A coefficient multiplying the operatorabelian (
bool
) – Indicates whether the Operators inoplist
are known to mutually commute.grad_combo_fn (
Optional
[Callable
]) – The gradient of recombination function. If None, the gradient will be computed automatically.that the default "recombination function" lambda above is essentially the (Note) –
 it accepts the list of values (identity) –
returns them in a list. (and) –

__init__
(oplist, combo_fn=None, coeff=1.0, abelian=False, grad_combo_fn=None)[source]¶  Parameters
oplist (
Sequence
[OperatorBase
]) – The list ofOperatorBases
defining this Operator’s underlying function.combo_fn (
Optional
[Callable
]) – The recombination function to combine classical results of theoplist
Operators’ eval functions (e.g. sum). Default is lambda x: x.coeff (
Union
[complex
,ParameterExpression
]) – A coefficient multiplying the operatorabelian (
bool
) – Indicates whether the Operators inoplist
are known to mutually commute.grad_combo_fn (
Optional
[Callable
]) – The gradient of recombination function. If None, the gradient will be computed automatically.that the default "recombination function" lambda above is essentially the (Note) –
 it accepts the list of values (identity) –
returns them in a list. (and) –
Methods
__init__
(oplist[, combo_fn, coeff, abelian, …]) type oplist
Sequence
[OperatorBase
]
add
(other)Return Operator addition of self and other, overloaded by
+
.adjoint
()Return a new Operator equal to the Operator’s adjoint (conjugate transpose), overloaded by
~
.assign_parameters
(param_dict)Binds scalar values to any Terra
Parameters
in the coefficients or primitives of the Operator, or substitutes oneParameter
for another.bind_parameters
(param_dict)Same as assign_parameters, but maintained for consistency with QuantumCircuit in Terra (which has both assign_parameters and bind_parameters).
compose
(other[, permutation, front])Return Operator Composition between self and other (linear algebrastyle: A@B(x) = A(B(x))), overloaded by
@
.copy
()Return a deep copy of the Operator.
ListOp default combo function i.e. lambda x: x.
equals
(other)Evaluate Equality between Operators, overloaded by
==
.eval
([front])Evaluate the Operator’s underlying function, either on a binary string or another Operator.
exp_i
()Return an
OperatorBase
equivalent to an exponentiation of self * i, e^(i*op).log_i
([massive])Return a
MatrixOp
equivalent to log(H)/i for this operator H.mul
(scalar)Returns the scalar multiplication of the Operator, overloaded by
*
, including support for Terra’sParameters
, which can be bound to values later (viabind_parameters
).neg
()Return the Operator’s negation, effectively just multiplying by 1.0, overloaded by

.permute
(permutation)Permute the qubits of the operator.
power
(exponent)Return Operator composed with self multiple times, overloaded by
**
.Return a set of strings describing the primitives contained in the Operator.
reduce
()Try collapsing the Operator structure, usually after some type of conversion, e.g.
tensor
(other)Return tensor product between self and other, overloaded by
^
.tensorpower
(other)Return tensor product with self multiple times, overloaded by
^
.Returns an equivalent Operator composed of only QuantumCircuitbased primitives, such as
CircuitOp
andCircuitStateFn
.to_matrix
([massive])Return NumPy representation of the Operator.
to_matrix_op
([massive])Returns an equivalent Operator composed of only NumPybased primitives, such as
MatrixOp
andVectorStateFn
.to_pauli_op
([massive])Returns an equivalent Operator composed of only Paulibased primitives, such as
PauliOp
.Returns SciPy sparse matrix representation of the Operator.
traverse
(convert_fn[, coeff])Apply the convert_fn to each node in the oplist.
Attributes
INDENTATION
Whether the Operators in
oplist
are known to commute with one another.The scalar coefficient multiplying the Operator.
The function defining how to combine
oplist
(or Numbers, or NumPy arrays) to produce the Operator’s underlying function.Indicates whether the ListOp or subclass is distributive under composition.
The gradient of
combo_fn
.Return the unique instance id.
The number of qubits over which the Operator is defined.
The list of
OperatorBases
defining the underlying function of this Operator.Return a set of Parameter objects contained in the Operator.
Return settings.

property
abelian
¶ Whether the Operators in
oplist
are known to commute with one another. Return type
bool
 Returns
A bool indicating whether the
oplist
is Abelian.

add
(other)[source]¶ Return Operator addition of self and other, overloaded by
+
. Parameters
other (
OperatorBase
) – AnOperatorBase
with the same number of qubits as self, and in the same ‘Operator’, ‘State function’, or ‘Measurement’ category as self (i.e. the same type of underlying function). Return type
ListOp
 Returns
An
OperatorBase
equivalent to the sum of self and other.

adjoint
()[source]¶ Return a new Operator equal to the Operator’s adjoint (conjugate transpose), overloaded by
~
. For StateFns, this also turns the StateFn into a measurement. Return type
ListOp
 Returns
An
OperatorBase
equivalent to the adjoint of self.

assign_parameters
(param_dict)[source]¶ Binds scalar values to any Terra
Parameters
in the coefficients or primitives of the Operator, or substitutes oneParameter
for another. This method differs from Terra’sassign_parameters
in that it also supports lists of values to assign for a giveParameter
, in which case self will be copied for each parameterization in the binding list(s), and all the copies will be returned in anOpList
. If lists of parameterizations are used, everyParameter
in the param_dict must have the same length list of parameterizations. Parameters
param_dict (
dict
) – The dictionary ofParameters
to replace, and values or lists of values by which to replace them. Return type
OperatorBase
 Returns
The
OperatorBase
with theParameters
in self replaced by the values orParameters
in param_dict. If param_dict contains parameterization lists, thisOperatorBase
is anOpList
.

bind_parameters
(param_dict)¶ Same as assign_parameters, but maintained for consistency with QuantumCircuit in Terra (which has both assign_parameters and bind_parameters).
 Return type
OperatorBase

property
coeff
¶ The scalar coefficient multiplying the Operator.
 Return type
Union
[complex
,ParameterExpression
] Returns
The coefficient.

property
combo_fn
¶ The function defining how to combine
oplist
(or Numbers, or NumPy arrays) to produce the Operator’s underlying function. For example, SummedOp’s combination function is to add all of the Operators inoplist
. Return type
Callable
 Returns
The combination function.

compose
(other, permutation=None, front=False)[source]¶ Return Operator Composition between self and other (linear algebrastyle: A@B(x) = A(B(x))), overloaded by
@
.Note: You must be conscious of Quantum Circuit vs. Linear Algebra ordering conventions. Meaning, X.compose(Y) produces an X∘Y on qubit 0, but would produce a QuantumCircuit which looks like
[Y][X]
Because Terra prints circuits with the initial state at the left side of the circuit.
 Parameters
other (
OperatorBase
) – TheOperatorBase
with which to compose self.permutation (
Optional
[List
[int
]]) –List[int]
which defines permutation on other operator.front (
bool
) – If front==True, returnother.compose(self)
.
 Return type
OperatorBase
 Returns
An
OperatorBase
equivalent to the function composition of self and other.

copy
()¶ Return a deep copy of the Operator.
 Return type
OperatorBase

property
distributive
¶ Indicates whether the ListOp or subclass is distributive under composition. ListOp and SummedOp are, meaning that (opv @ op) = (opv[0] @ op + opv[1] @ op) (using plus for SummedOp, list for ListOp, etc.), while ComposedOp and TensoredOp do not behave this way.
 Return type
bool
 Returns
A bool indicating whether the ListOp is distributive under composition.

equals
(other)[source]¶ Evaluate Equality between Operators, overloaded by
==
. Only returns True if self and other are of the same representation (e.g. a DictStateFn and CircuitStateFn will never be equal, even if their vector representations are equal), their underlying primitives are equal (this means for ListOps, OperatorStateFns, or EvolvedOps the equality is evaluated recursively downwards), and their coefficients are equal. Parameters
other (
OperatorBase
) – TheOperatorBase
to compare to self. Return type
bool
 Returns
A bool equal to the equality of self and other.

eval
(front=None)[source]¶ Evaluate the Operator’s underlying function, either on a binary string or another Operator. A square binary Operator can be defined as a function taking a binary function to another binary function. This method returns the value of that function for a given StateFn or binary string. For example,
op.eval('0110').eval('1110')
can be seen as querying the Operator’s matrix representation by row 6 and column 14, and will return the complex value at those “indices.” Similarly for a StateFn,op.eval('1011')
will return the complex value at row 11 of the vector representation of the StateFn, as all StateFns are defined to be evaluated from Zero implicitly (i.e. it is as if.eval('0000')
is already called implicitly to always “indexing” from column 0).ListOp’s eval recursively evaluates each Operator in
oplist
, and combines the results using the recombination functioncombo_fn
. Parameters
front (
Union
[str
,Dict
[str
,complex
],ndarray
,OperatorBase
,Statevector
,None
]) – The bitstring, dict of bitstrings (with values being coefficients), or StateFn to evaluated by the Operator’s underlying function. Return type
Union
[OperatorBase
,complex
] Returns
The output of the
oplist
Operators’ evaluation function, combined with thecombo_fn
. If either self or front contain properListOps
(not ListOp subclasses), the result is an ndimensional list of complex or StateFn results, resulting from the recursive evaluation by each OperatorBase in the ListOps. Raises
NotImplementedError – Raised if called for a subclass which is not distributive.
TypeError – Operators with mixed hierarchies, such as a ListOp containing both PrimitiveOps and ListOps, are not supported.
NotImplementedError – Attempting to call ListOp’s eval from a nondistributive subclass.

exp_i
()[source]¶ Return an
OperatorBase
equivalent to an exponentiation of self * i, e^(i*op). Return type
OperatorBase

property
grad_combo_fn
¶ The gradient of
combo_fn
. Return type
Optional
[Callable
]

property
instance_id
¶ Return the unique instance id.
 Return type
int

log_i
(massive=False)[source]¶ Return a
MatrixOp
equivalent to log(H)/i for this operator H. This function is the effective inverse of exp_i, equivalent to finding the Hermitian Operator which produces self when exponentiated. For proper ListOps, applieslog_i
to all ops in oplist. Return type
OperatorBase

mul
(scalar)[source]¶ Returns the scalar multiplication of the Operator, overloaded by
*
, including support for Terra’sParameters
, which can be bound to values later (viabind_parameters
). Parameters
scalar (
Union
[complex
,ParameterExpression
]) – The real or complex scalar by which to multiply the Operator, or theParameterExpression
to serve as a placeholder for a scalar factor. Return type
ListOp
 Returns
An
OperatorBase
equivalent to product of self and scalar.

neg
()¶ Return the Operator’s negation, effectively just multiplying by 1.0, overloaded by

. Return type
OperatorBase
 Returns
An
OperatorBase
equivalent to the negation of self.

property
num_qubits
¶ The number of qubits over which the Operator is defined. If
op.num_qubits == 5
, thenop.eval('1' * 5)
will be valid, butop.eval('11')
will not. Return type
int
 Returns
The number of qubits accepted by the Operator’s underlying function.

property
oplist
¶ The list of
OperatorBases
defining the underlying function of this Operator. Return type
List
[OperatorBase
] Returns
The Operators defining the ListOp

property
parameters
¶ Return a set of Parameter objects contained in the Operator.

permute
(permutation)[source]¶ Permute the qubits of the operator.
 Parameters
permutation (
List
[int
]) – A list defining where each qubit should be permuted. The qubit at index j should be permuted to position permutation[j]. Return type
OperatorBase
 Returns
A new ListOp representing the permuted operator.
 Raises
OpflowError – if indices do not define a new index for each qubit.

power
(exponent)[source]¶ Return Operator composed with self multiple times, overloaded by
**
. Return type
OperatorBase

primitive_strings
()[source]¶ Return a set of strings describing the primitives contained in the Operator. For example,
{'QuantumCircuit', 'Pauli'}
. For hierarchical Operators, such asListOps
, this can help illuminate the primitives represented in the various recursive levels, and therefore which conversions can be applied. Return type
Set
[str
] Returns
A set of strings describing the primitives contained within the Operator.

reduce
()[source]¶ Try collapsing the Operator structure, usually after some type of conversion, e.g. trying to add Operators in a SummedOp or delete needless IGates in a CircuitOp. If no reduction is available, just returns self.
 Return type
OperatorBase
 Returns
The reduced
OperatorBase
.

property
settings
¶ Return settings.
 Return type
Dict

tensor
(other)[source]¶ Return tensor product between self and other, overloaded by
^
. Note: You must be conscious of Qiskit’s bigendian bit printing convention. Meaning, X.tensor(Y) produces an X on qubit 0 and an Y on qubit 1, or X⨂Y, but would produce a QuantumCircuit which looks like[Y] [X]
Because Terra prints circuits and results with qubit 0 at the end of the string or circuit.
 Parameters
other (
OperatorBase
) – TheOperatorBase
to tensor product with self. Return type
OperatorBase
 Returns
An
OperatorBase
equivalent to the tensor product of self and other.

tensorpower
(other)[source]¶ Return tensor product with self multiple times, overloaded by
^
. Parameters
other (
int
) – The int number of times to tensor product self with itself viatensorpower
. Return type
Union
[OperatorBase
,int
] Returns
An
OperatorBase
equivalent to the tensorpower of self by other.

to_circuit_op
()[source]¶ Returns an equivalent Operator composed of only QuantumCircuitbased primitives, such as
CircuitOp
andCircuitStateFn
. Return type
OperatorBase

to_matrix
(massive=False)[source]¶ Return NumPy representation of the Operator. Represents the evaluation of the Operator’s underlying function on every combination of basis binary strings. Warn if more than 16 qubits to force having to set
massive=True
if such a large vector is desired. Return type
ndarray
 Returns
The NumPy
ndarray
equivalent to this Operator.

to_matrix_op
(massive=False)[source]¶ Returns an equivalent Operator composed of only NumPybased primitives, such as
MatrixOp
andVectorStateFn
. Return type
ListOp

to_pauli_op
(massive=False)[source]¶ Returns an equivalent Operator composed of only Paulibased primitives, such as
PauliOp
. Return type
ListOp

to_spmatrix
()[source]¶ Returns SciPy sparse matrix representation of the Operator.
 Return type
Union
[spmatrix
,List
[spmatrix
]] Returns
CSR sparse matrix representation of the Operator, or List thereof.

traverse
(convert_fn, coeff=None)[source]¶ Apply the convert_fn to each node in the oplist.
 Parameters
convert_fn (
Callable
) – The function to apply to the internal OperatorBase.coeff (
Union
[complex
,ParameterExpression
,None
]) – A coefficient to multiply by after applying convert_fn. If it is None, self.coeff is used instead.
 Return type
ListOp
 Returns
The converted ListOp.